U.S. patent number 5,869,759 [Application Number 08/701,871] was granted by the patent office on 1999-02-09 for method and apparatus for regional gravity surveys using a gps receiver.
Invention is credited to Harold O. Seigel.
United States Patent |
5,869,759 |
Seigel |
February 9, 1999 |
Method and apparatus for regional gravity surveys using a GPS
receiver
Abstract
Method and apparatus for conducting regional gravity surveys,
comprising a gravimeter module suspended below a helicopter and
adapted to be lowered to the earth's surface for generating
gravimeter readings. The gravimeter module includes an automatic
reading gravimeter sensor and a mechanism for self-levelling of the
sensor. A ground contact sensor is provided for determining when
the gravimeter module contacts the earth's surface as a result of
being lowered thereto and for determining when the gravimeter
module ceases contacting the earth's surface as a result of being
raised therefrom. The ground contact sensor generates a time marker
indicative of these events. A GPS receiver is mounted in fixed
relationship with the helicopter for generating periodic position
coordinates. A system is provided for receiving and recording the
subsurface gravimeter readings, the periodic position coordinates,
and the time marker on a common time base. The system further
includes circuitry for calculating the position coordinates of the
gravimeter module when the gravimeter module contacts the earth's
surface and when the module ceases contacting the earth's surface,
by means of interpolating between respective values of the periodic
position coordinates at the generated time markers.
Inventors: |
Seigel; Harold O. (North York,
Ontario, CA) |
Family
ID: |
24819016 |
Appl.
No.: |
08/701,871 |
Filed: |
August 23, 1996 |
Current U.S.
Class: |
73/382R |
Current CPC
Class: |
G01V
7/16 (20130101) |
Current International
Class: |
G01V
7/00 (20060101); G01V 7/16 (20060101); G01V
007/16 () |
Field of
Search: |
;73/382R,382G
;364/449.7,449.9 ;342/457 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Will Featherstone, Curtin University of Technology & Mike
Dentith, The University of Western Australia, Matters of Gravity:
The Search for Gold, 1994 (no month)..
|
Primary Examiner: Oda; Christine K.
Claims
I claim:
1. Apparatus for conducting helicopter-supported gravity surveys of
a survey area, comprising:
a gravimeter module suspended below a helicopter and adapted to be
lowered to the earth's surface for generating gravimeter readings,
said gravimeter module including an automatic reading gravimeter
sensor and means for self-levelling said sensor;
a ground contact sensor for determining when said gravimeter module
contacts the earth's surface as a result of being lowered thereto,
and in response generating a time marker indicative thereof;
a GPS receiver mounted in fixed relationship to said helicopter for
generating periodic position coordinates; and
a system for receiving and recording said gravimeter readings, said
periodic position coordinates and said time marker on a common time
base.
2. Apparatus for conducting helicopter-supported gravity surveys of
a survey area, comprising:
a gravimeter module suspended below a helicopter and adapted to be
lowered to the earth's surface for generating gravimeter readings,
said gravimeter module including an automatic reading gravimeter
sensor and means for self-levelling said sensor;
a ground contact sensor for determining when said gravimeter module
ceases contacting the earth's surface as a result of being raised
therefrom subsequent to generation of said gravimeter readings, and
in response generating a time marker indicative thereof;
a GPS receiver mounted in fixed relationship to said helicopter for
generating periodic position coordinates; and
a system for receiving and recording said gravimeter readings, said
periodic position coordinates and said time marker on a common time
base.
3. The apparatus of claim 1, wherein said system further includes
means for calculating the position of said gravimeter module when
said gravimeter module contacts the earth's surface, by means of
interpolating between respective values of said periodic position
coordinates at said time marker.
4. The apparatus of claim 2, wherein said system further includes
means for calculating the position of said gravimeter module when
said gravimeter module ceases contacting the earth's surface, by
means of interpolating between respective values of said periodic
position coordinates at said time marker.
5. The apparatus of claim 1, further comprising three legs
projecting from a bottom surface of said gravimeter module, and
three contact switches connected to respective ones of said legs,
whereby upon closure of all of said contact switches said time
marker is generated.
6. The apparatus of claim 2, further comprising three legs
projecting from a bottom surface of said gravimeter module, and
three contact switches connected to respective ones of said legs,
whereby upon opening of any one of said contact switches said time
marker is generated.
7. The apparatus of claim 1 or 2, further including a proximity
sensor mounted to said gravimeter module for indicating distance of
said gravimeter module above the earth's surface.
8. The apparatus of claim 3 or 4, further including a farther GPS
receiver located at a predetermined fixed location on the earth's
surface and in the vicinity of said survey area for providing
information in response to which said system corrects its
calculation of said position of the gravimeter module to account
for ionospheric effects.
9. The apparatus of claim 1 or 2, further including a water
pressure monitor for determining water depth of said gravimeter
module when said module is lowered into water below the earth's
surface.
10. The apparatus of claim 1 or 2, further including a water
immersion sensor for generating further time markers upon entry of
said gravimeter module into water and emergence of said module
therefrom.
11. The apparatus of claim 1 or 2, wherein said means for
self-levelling said sensor includes pendulum means for rapid coarse
levelling and motor driven means controlled by the output of level
sensors rigidly mounted on said gravimeter sensor, to achieve fine
levelling.
12. A method of conducting helicopter-supported gravity surveys,
comprising the steps of:
suspending a self-levelling automatic reading gravimeter sensor
from a helicopter, said sensor being capable of generating
gravimeter readings when in contact with the earth's surface;
lowering said gravimeter sensor to the earth's surface;
determining the GPS relative coordinates of said gravimeter sensor
while said gravimeter sensor is being lowered;
generating a time marker in response to said sensor contacting the
earth's surface;
levelling said gravimeter sensor and obtaining said gravimeter
readings therefrom while said gravimeter sensor is in contact with
the earth's surface and said helicopter hovers overhead; and
recording said gravimeter readings, said GPS relative coordinates
and said time marker on a common time base.
13. A method of conducting helicopter-supported gravity surveys,
comprising the steps of
suspending a self-levelling automatic reading gravimeter sensor
from a helicopter, said sensor being capable of generating
gravimeter readings when in contact with the earth's surface;
lowering said gravimeter sensor to the earth's surface;
levelling said gravimeter sensor and obtaining said gravimeter
readings therefrom while said gravimeter sensor is in contact with
the earth's surface and said helicopter hovers overhead;
raising said gravimeter sensor from the earth's surface subsequent
to generation of said gravimeter readings;
determining the GPS relative coordinates of said gravimeter sensor
while said gravimeter sensor is being raised;
generating a time marker in response to said sensor ceasing to be
in contact with the earth's surface; and
recording said gravimeter readings, said GPS relative coordinates
and said time markers on a common time base.
14. The method of claim 12 or 13, further comprising the step of
determining the elevation of said gravimeter sensor on the earth's
surface by interpolating said GPS relative coordinates before and
after said time marker.
15. The method of claim 14, further comprising the step of
correcting said determining of the elevation of said gravimeter
sensor to account for ionospheric effects.
16. The method of claim 14, wherein said step of interpolating
comprises fitting at least two of said GPS relative coordinates
before and after said time marker onto a polynomial function of
elevation versus time and calculating for said elevation at a time
equal to said time marker.
17. The method of claim 12 or 13, further comprising the steps of
immersing said gravimeter sensor in water below the earth's surface
and determining water depth by means of a water pressure
monitor.
18. The method of claim 17, further comprising the step of
recording when said gravimeter sensor is immersed in said
water.
19. The method of claim 17, further comprising the step of lifting
said gravimeter sensor out of said water.
20. The method of claim 19, further comprising the step of
recording when said gravimeter sensor emerges from said water.
21. The method of claims 12 or 13 wherein said gravimeter sensor is
levelled in two stages, firstly, in a coarse but rapid fashion by
pendulum action and then by motor driven means, controlled by the
output of level sensors which are rigidly mounted on the gravimeter
sensor.
Description
FIELD OF THE INVENTION
This invention relates in general to gravity surveying and more
particularly to a method and apparatus for conducting
helicopter-suspended, land-gravimeter surveys, using precise GPS
positioning, whereby accurate gravity measurements can be made in a
rapid and cost effective fashion, without any requirement for the
helicopter to land at each station.
BACKGROUND TO THE INVENTION
Gravimetry is a well known method of mapping subsurface geology
utilizing potential fields, for resource development purposes.
Although gravimetry is well known in the art, its application and
use to date have been restricted by cost considerations relating to
the cost of determining station elevation. Gravimeter measurements,
per se, are largely meaningless unless accompanied by an accurate
determination of the relative elevation of each station. To be
consistent with the accuracy of modern first order gravimeters such
as those manufactured by Scintrex Limited or La Coste, the
determination of station elevation traditionally requires the
application of optical levelling. Optical levelling is a slow
process and is costly for determining the elevation of widely
spaced stations (eg. 1 km or more apart), or when applied in rugged
or forested areas. By way of contrast, gravimeter readings
themselves are fast, typically requiring only 2-3 minutes per
station, and they constitute only a minor portion of the total
survey cost where optical levelling is employed. Other means of
determining station elevation, such as the use of micro-barometric
altimeters, result in much lower accuracy (typically .+-.1 m to
.+-.3 m in elevation, equivalent to .+-.0.03 mGals to .+-.1 mGals
in gravity).
Recent developments in the design of differential GPS (Global
Positioning System) receivers has resulted in the ability to obtain
high accuracy gravimeter station elevation calculations. For
example, Fetherstone and Dentith, "Matters of Gravity: The Search
for Gold", GPS World, July 1994, have shown that a standard
deviation (SD) of a measurement of 2.2 cm can be realized by such
means. In terms of speed and cost, this represents a major advance
in the field of gravity surveying where the stations are more than
500 m apart.
The use of helicopters to transport and position gravimeter crews
has also been well known in the art for several decades. The
efficiency of this practice, however, relies heavily on the
availability of suitable landing sites which are conveniently
located in proximity to the desired station locations. This,
unfortunately, is not always the case, particularly where the
stations are located in rugged topography, water covered or in
marshland, in closely spaced tree cover, etc. In some areas, there
are prohibitions against landing, due to hazards or to protect
delicate environmental biosystems, etc.
SUMMARY OF THE INVENTION
It is an object of an aspect of this invention to provide a highly
cost effective, rapid and accurate means for performing
helicopter-supported, regional or semi-detailed gravity surveys, in
otherwise difficult areas, without the necessity for the helicopter
to land at each station. It is a further object of an aspect of the
invention to provide a method of obtaining low-cost and rapid
determination of station elevation.
Therefore, in accordance with the present invention, there is
provided an apparatus for conducting helicopter-supported gravity
surveys, comprising a gravimeter module suspended below a
helicopter and adapted to be lowered to the earth's surface for
generating gravimeter readings. The gravimeter module includes an
automatic reading gravimeter sensor and a mechanism for
self-levelling of the sensor. A ground contact sensor is provided
for determining when the gravimeter module contacts the earth's
surface as a result of being lowered thereto and for determining
when the gravimeter module ceases contacting the earth's surface as
a result of being raised therefrom. The ground contact sensor
generates a time marker indicative of these events. A GPS receiver
is mounted in fixed relationship with the helicopter for generating
periodic position coordinates. A control and data acquisition
system is provided for receiving and recording the gravimeter
readings, the periodic position coordinates, and the time marker on
a common time base. The control and data acquisition system further
includes circuitry for calculating the position of the gravimeter
module when the gravimeter module contacts the earth's surface and
when the module ceases contacting the earth's surface, by means of
interpolating between the periodic GPS position coordinates before
and after the generated time markers.
BRIEF DESCRIPTION OF THE DRAWINGS
A detailed description of the invention is provided herein below
with reference to the following, in which:
FIG. 1 shows an apparatus for conducting helicopter-supported
gravity surveys in accordance with the present invention,
FIG. 2 is a block diagram showing component parts of the apparatus
according to the present invention;
FIG. 3 is a graph showing calculation of station elevation of a
gravimeter station according to the method of the present
invention;
FIG. 4 shows the apparatus of the present invention in use on
shallow-water covered areas; and
FIG. 5 illustrates, in greater detail, the operation of the
self-levelling system.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
Turning to FIGS. 1, a gravimeter module 1 is shown suspended below
a helicopter 2 by a tow and communication cable 3. The gravimeter
module contains a gravimeter sensor 4 and a self-levelling,
dual-gimbal system 5. External to the gravimeter module is a ground
contact sensor 6, a ground proximity sensor 7, a water pressure
monitor 8, and a water immersion sensor 9.
FIG. 2 shows the component parts of the system gravimeter module 1
and its connection to equipment onboard the helicopter 2. The
dual-gimbal system 5 is shown comprising gravimeter system 4, level
sensors 10 rigidly mounted to the gravimeter sensor 4 and a pair of
servo motors 11. The level sensors 10, generate output signals
which are proportional to the offset angle of the gravimeter sensor
4, from vertical. These signals control the servo motors 11, which,
in turn, level the gravimeter sensor. This system operates
essentially as a closed feed-back loop.
FIG. 5 shows, in somewhat greater detail, the operation of the
self-levelling system. The two level sensors 10 are mounted and
adjusted so as to be orthogonal to each other and to the mechanical
(vertical) axis of the gravimeter sensor 4. Each level sensor 10
provides a DC signal output which, in sign and amplitude, gives an
indication of the deviation of its axis from horizontal, in
direction and amount. These signal outputs provide the measure of
the deviation of the mechanical axis of the gravimeter sensor 4
from the true plump-bob vertical. The dynamic range of these level
sensors 10 is typically .+-.1500 arc seconds, and their resolution
is typically 1 arc second.
The precision required in levelling is determined by the need to
measure the relative value of gravity to better than 5 .mu.Gals. In
terms of effective precision of alignment to the vertical, this
means that the alignment error angle .crclbar. must satisfy the
equation 1-cos.sup.2 .crclbar.<5.times.10.sup.-9 (i.e.,
.crclbar.<20 arc seconds).
The gravimeter module 1 may come to rest at a substantial
inclination to the horizontal, because of irregularities of the
ground surface. The system of the present invention is intended to
allow for inclinations of up to 36.degree. from the horizontal. The
design of the self-levelling system is such as to accommodate such
large inclinations, and yet perform the self-levelling to the
required precision (<20 arc seconds) within less than 10
seconds.
In order to do so a two stage system is employed, including firstly
a gravity-based pendulum action and then a servo-motor-based
action.
As FIG. 5 shows, the centre of gravity C of the gravimeter sensor 4
is at a distance L below the central point of suspension of the
sensor. When the gravimeter assembly 1 comes to rest on the
surface, activating the ground contact sensor 6, the signal from
this sensor releases the clutches on the servo motors 11 allowing
the gravimeter sensor 4 to seek the vertical, as a pendulum,
According to the theory of simple pendulums, the period of
oscillation of a pendulum is given by ##EQU1## where L is in meters
and g is the acceleration of gravity (10 m/s.sup.2). For L=0.1 m,
for example, T=0.6 seconds. This means that regardless of the
inclination of the gravimeter sensor 4 from vertical at the landing
site, once the clutches are released, the gravimeter sensor 4 will
pass through vertical in time T/4, or 0.15 seconds in this case.
Thus, by re-engaging the clutches of the servo motors 11 at a time
T/4 after their final initial release, the gravimeter sensor will
be quite close to its required verticality. Thereupon the servo
motors 11 are activated, each under the control of its respective
level sensor 10, to achieve the ultimate precision of levelling
(e.g. <20 arc seconds).
Alternatively, the clutches may be briefly reactivated several
times on the initial pendulum swing, e.g., at T/8 intervals, to
reduce the maximum angular momentum of the gravimeter sensor and
therefore, the stresses on the clutches.
In this manner, even with several short activations of the
clutches, the gravimeter sensor 4 may be brought close to vertical,
well within the range of the level sensor 20 within one second.
Thereafter, the clutches are engaged and, under the control of the
level sensor 10, the servo motors 11 may bring the gravimeter
sensor 4 into vertical within the desired .+-.20 arc second
range.
The output signals from ground contact sensor 6, are provided to
both the gravimeter and to a control and data acquisition system
12, disposed in the helicopter, via communication cable 3. The
outputs of all other sensors in or on the gravimeter module 1 are
transmitted via the cable 3 to the control and data acquisition
system 12, in the helicopter 2.
A radar altimeter 13, located in the helicopter, provides
quantitative information on the height of the helicopter above
ground. A high accuracy GPS receiver 14, (preferably a
dual-frequency, carrier-phase device) is mounted on the helicopter
to provide rapid periodic updates of the spatial coordinates of the
helicopter. A display screen 15, provides all pertinent information
to the pilot or operator. A further reference GPS receiver 16, is
preferably located in a fixed position near the survey area to
provide corrections for ionospheric changes on the moving GPS
receiver 14, either in real time by radio link, or off-line. More
particularly, the distance measurement signals received from the
satellites (usually at least four or five satellites being
monitored at one time) are affected by changes in the ionosphere
which can lead to erroneous information. By subtracting the
location information generated by the secondary fixed GPS receiver
16 (within 50 km of the survey area) from the airborne receiver 14,
relative position coordinates are obtained and the effects of
ionospheric changes are cancelled. We have found that suitable GPS
receivers for this purpose are, for example, the Turbo Rogue
receivers, manufactured by Allan Osborne Associates, Inc.
It is contemplated that the design of the gravimeter module 1 be
based on the well-proven Scintrex CG-3 Autograv.TM., automated
portable land gravimeter. This system incorporates a quartz element
sensor which is extremely rugged, and is able to withstand shocks
of up to 25 g without damage, and without offsets greater than 0.02
mGals. The system has no requirement for clamping between readings
and is compatible with helicopter vibrations in transport. The
enclosure into which the gravimeter assembly is mounted is
hermetically sealed, and is rated for immersion in water up to more
than 10 m deep.
In survey operations, the GPS receiver 14, maintains kinematic lock
with at least four GPS satellites in flight, thereby providing the
spatial coordinates of the helicopter (latitude, longitude and
altitude), commonly at one second update intervals, at all times.
Reliable coordinate generation requires that the receivers have an
essentially clear view of the sky at all times (ie. 2.pi. field of
view). Whereas, ideally, the most appropriate position of the GPS
receiver 14, would be directly on the gravimeter module 1, in order
to establish the exact coordinates of the gravimeter sensor 4, in
practice, this is rarely feasible due to tree shading and hills in
most areas. In addition, if the GPS receiver 14 is mounted directly
on the gravimeter module 1, it is not possible to utilize the
system in shallow water-covered areas, such as lakes, rivers,
swamps, and sea-coasts.
According to the present invention, the GPS receiver 14, is mounted
on the helicopter 2, or on the tow cable 3 at a very short distance
below the helicopter. Of course, in order to maintain kinematic
lock in this case, the helicopter 2 must have an uninterrupted view
of the sky at all times. This necessitates that the helicopter
maintain sufficient terrain clearance as to avoid all obstacles. In
many areas, this imposes the condition that the helicopter remain
aloft while conducting the survey. For survey operations, the cable
3 may be up to 30 m long for light helicopters like the Hughes 500,
or as much as 50 m for heavier helicopters such as the Aerostar
AS-350 B-2, which is especially useful in water-covered areas.
The entire system according to the present invention is fully
automated and software controlled, such that the pilot is required
only to respond to instructions on the display screen 15. All
decisions about data quality, for example, are made by the software
implemented by the system, as discussed in greater detail below
with reference to FIG. 5.
At the start of a survey operation, the helicopter 2 and gravimeter
module 1 are both on the ground and are interconnected by the cable
3. First, the helicopter takes off, rising vertically above the
gravimeter module 1, and lifts it off of the ground. The helicopter
then continues to rise to a transit level (eg. 100 m to 150 m)
above the ground and proceeds to its first designated gravity
station, under GPS guidance.
When, under GPS guidance, the helicopter 2, arrives at the location
of a predetermined gravimeter station, the pilot seeks out the
nearest suitable site for the station (eg. an opening in the trees)
which is as free as possible of local topographic irregularities.
The pilot then reduces his elevation, slowly lowering the
gravimeter module 1 to the ground using the proximity sensor 7 as a
guide to a soft landing. The proximity sensor is designed to
provide a quantative estimate of the distances of the gravimeter
module from the nearest ground point or water surface, with an
accuracy of about 10 cm, from 0 to 10 m. A suitable such sensor is
the 9000 Series, Piezo Transducer, manufacture by Polaroid
Corporation. Lowering of the gravimeter module 1 to ground is
followed, automatically, by the gravimeter measurements themselves.
When all three legs of the tripod ground contact sensor 6 are on
the ground, a signal is generated thereby and is transmitted to the
gravimeter module 1 to activate the self-levelling process.
As discussed above, in order to obtain accurate gravimeter
readings, the relative elevation of the gravimeter must be
calculated in order to apply the usual correction for elevation.
This correction is given by the formula Ce=+(0.3086-0.0419 d) h, in
mGals, where d is the density of the near-surface rocks, in
g/cm.sup.3, and h is the elevation of the gravity sensor in m.,
relative to a predetermined datum level (eg. the elevation of GPS
receiver 16).
For high precision regional gravity measurements (eg. correct to
0.02 mGals) a determination of h to within 10 cm relative accuracy
is required. As indicated above, it is feasible to achieve this
relative accuracy of elevation by means of modern GPS receivers.
However, since the moving GPS receiver 14 is on the helicopter 2,
and the gravimeter module 1 is on the ground, a problem arises of
determining the relative elevation of the gravimeter and the GPS
receiver on the helicopter, to within the required accuracy.
Several solutions may exist, including the use of electro-optical
distance-ranging devices such as microwave or laser-based systems,
etc. However, these devices are costly and complex in operation,
and are difficult to automate.
The system of the present invention provides a solution to this
problem. When the pilot is over the selected station and is
descending, the tow cable 3 bears the weight of the gravimeter
module 1, and functions, therefore, as a vertical "plumb-bob". In
this condition, the vertical distance between the gravimeter sensor
1 and the GPS receiver 14, on the helicopter, is predictably
constant to within the required accuracy of 10 cm., provided that
the tow cable 3 remains within 4.degree. of verticality. This
distance remains constant, in fact, until the tension on the cable
3 is reduced by the gravimeter module contacting the ground. This
occurs at the precise moment when the last of the three legs of the
tripod on which the gravimeter module 1 is mounted touches firmly
down. This is also the moment at which the ground contact sensor 6
is activated. The ground contact sensor 6 is so designed as to be
activated only when all three legs of the tripod supporting the
gravimeter module 1 have come to rest on the ground. The reason for
this requirement is that when landing on an inclined surface the
gravimeter sensor has not assumed its true elevation until all
three legs are on the ground.
To achieve this requirement, the ground contact sensor 6 is made to
consist of three individual contact sensors, one on each leg of the
tripod. For simplicity, these may be connected in series, so that
the sensor will be activated only when all three component sensors
are so activated.
A suitable sensor component for this purpose, on each leg, may, for
example, be the AU-PB-SD-C push button switch manufacture by
Giannini Petro-Marine, Inc. which is both waterproof and sealed
against mud, etc.
According to the present invention, a time marker is generated upon
impact of the gravimeter module 1 with the ground. This time marker
is sent to the controudata acquisition system 12, where its time is
recorded, relative to the GPS clock time base.
GPS receivers are commonly programmed to provide coordinate updates
at regular intervals, typically one second. The ground contact time
markers will, of course, generally occur somewhere between two
successive GPS updates. In order to determine the coordinates of
the gravimeter 1 at the precise moment of landing it is necessary
to interpolate between successive GPS coordinates.
Since the vertical velocity of the helicopter 2 is not constant in
the interval spanning the landing of the gravimeter module 1 (eg.
the pilot typically decelerates the helicopter in response to
information from the proximity sensor 7), this interpolation is not
linear. It therefore requires the use of a higher order polynomial,
(eg. 3.sup.rd order polynomial), using two or more GPS coordinates
before and after the contact time marker, in order to determine the
coefficients of the polynomial.
The ground contact time marker is also presented on the display
screen 15, for the information of the pilot. The pilot then
descends a few metres, to provide enough slack on the cable 3, to
allow a portion of the cable to lie on the ground, thereby
decoupling any vibrations that might otherwise be transmitted down
the cable 3 to the gravimeter sensor 4. The pilot then hovers while
the system completes the gravimeter measurement (eg. typically
20-30 seconds duration).
Once the gravity measurement has been completed, with satisfactory
accuracy as determined by the software, a signal is sent to the
controudata acquisition console 12, and by it to the display screen
15 to indicate completion of the survey data acquisition. We have
found that the DATA 1 data acquisition system, manufactured by
Scintrex Limited, is suitable for this purpose. The pilot then
lifts off, carrying the gravimeter module 1 to the next
predetermined station. At the exact instant that the tow cable 3
becomes taut (ie. when the first of the three tripod legs ceases
contacting the ground), the ground sensor 6 transmits another
timing signal. This time marker provides a second measure, by
interpolation, of the coordinates of the gravimeter module 1 on the
ground at the moment of lift-off.
FIG. 3 illustrates the method by which precise elevation of the
gravimeter station may be determined from a non-linear (eg.
3.sup.rd order polynomial) interpolation between periodic (eg. 1
second) GPS coordinate updates, both on landing and take-off of the
gravimeter module 1. The coefficients of the two polynomials, in
this case, are based on fitting the two GPS coordinate updates
before and after the landing and take-off time markers.
The determination of the four coefficients of a polynomial of the
3.sup.rd order which passes through four consecutive 1 second GPS
elevation coordinate values may be accomplished as follows:
The polynomial may be represented by the expression:
Z=A+Bt+Ct.sup.2 +Dt.sup.3, where t is the time of the GPS
measurement. For simplicity, the value of t may be taken to be zero
at the first coordinate measurement.
It can be seen that A=Zo, i.e., the first GPS elevation (at time
t=0). There are then three equations in the three unknowns, B, C
and D, for the elevations at the three succeeding one second
times:
and
These equations are readily inverted, to provide values of the
coefficients, as follows:
and
For the example shown in FIG. 3, the polynomial representing the
elevation curve at the landing time maker is
H1=540-0.52t+0.063t.sup.2 +0.002t.sup.3, while the polynomial
representing the elevation curve at the lift-off time marker is
H.sub.2 =538+0.83(t-35)+0.086(t-35).sup.2 +0.0084(t-35).sup.3.
FIG. 4 shows the system of the present invention in operation at a
station which is covered with shallow water. The only physical
change required to the system for such use, is the addition of
weights at the base of the gravimeter module 1, so that it has
sufficient negative buoyancy as to sink rapidly to the bottom of
the water.
For this application, a water immersion sensor 9, provides time
markers at the moment of immersion and emergence, which permit the
determination of the GPS elevation of the water surface. We have
found that a suitable sensor for those purpose is the LV 11 Water
Level Sensor, manufactured by Omega, Inc. When the module comes to
rest on the bottom, the ground contact sensor 6 provides a time
marker in the usual manner, in order to allow the determination of
the relative elevation of the station. However, the water pressure
monitor 8, provides an independent indication of the water depth at
the station which, when coupled with the elevation of the water
surface, gives still another measure of the relative elevation of
the station. We have found that a suitable water pressure monitor
is the PX216-030 AI model, manufactured by Omega, Inc.
Knowledge of the depth of water at the station is required in order
to correct for the negative gravity effect of the water lying over
the gravimeter sensor 4, at the station. The appropriate correction
is given by Cw=+0.0419 w, measured in mgals, where w is the
overlying water depth, in m.
When the station is water-covered as shown in FIG. 4, the proximity
sensor 7 serves to provide the pilot with distance information to
the water surface, thereby assisting the pilot to ensure a soft
landing on the water.
Other embodiments and modifications of the invention are possible
without departing from the sphere and scope defined by the claims
appended hereto.
* * * * *